Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/71165
標題: On characterization and perturbation of local C-semigroups
作者: Li, Y.C.
Shaw, S.Y.
關鍵字: local C-semigroup
(C-0)-group
generator
perturbation
cauchy-problem
regularized semigroups
cosine functions
theorem
期刊/報告no:: Proceedings of the American Mathematical Society, Volume 135, Issue 4, Page(s) 1097-1106.
摘要: Let S(center dot) be a (C-0)- group with generator -B, and let {T(t); 0 <= t <tau} be a local C-semigroup commuting with S(center dot). Then the operators V(t):= S(-t)T(t), 0=t <tau, form a local -semigroup. It is proved that if C is injective and A is the generator of T(center dot), then A+B is closable and (A+B) over bar is the generator of V(center dot). Also proved are a characterization theorem for local C-semigroups with C not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem: u'(t)=Au(t)+Cf( t), 0 < t < t; u(0)=Cx.
URI: http://hdl.handle.net/11455/71165
ISSN: 0002-9939
文章連結: http://dx.doi.org/10.1090/s0002-9939-06-08549-2
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